Automated discovery of fundamental variables hidden in experimental data

Area of Science:

• Physics
• Data Science
• Dynamical Systems

Background:

• Physical laws are mathematical relationships between state variables, crucial for system description.
• Identifying these hidden state variables from observational data remains a significant challenge for automated methods.
• Current data-driven modeling often requires prior knowledge of the system's state variables.

Purpose of the Study:

• To propose a principle for determining the number and identity of state variables from high-dimensional observational data.
• To develop an automated method for discovering hidden state variables without prior physical knowledge.
• To address the longstanding question of identifying state variables solely from observed data.

Main Methods:

• Developing a novel principle to infer the intrinsic dimension of observed dynamics.
• Applying an algorithm to video recordings of diverse physical dynamical systems.
• Utilizing high-dimensional observational data without pre-existing physical models.

Main Results:

• Successfully determined the intrinsic dimension of various observed dynamical systems.
• Identified candidate sets of relevant state variables for different physical phenomena.
• Demonstrated the algorithm's effectiveness on systems like elastic double pendulums and fire flames.

Conclusions:

• The proposed principle offers a viable method for automated state variable discovery.
• This approach can significantly enhance data-driven modeling in physics and other sciences.
• Enables uncovering the fundamental descriptive variables of complex systems from raw observations.